LMFDB - Embedded newform 588.4.k.e.521.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,4,Mod(509,588)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("588.509");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	588.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$34.6931230834$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.22
Character	$\chi$	$=$	588.521
Dual form			588.4.k.e.509.22

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.14452 - 0.730696i) q^{3} +(3.83273 + 6.63849i) q^{5} +(25.9322 - 7.51816i) q^{9} +O(q^{10})$	\(q+(5.14452 - 0.730696i) q^{3} +(3.83273 + 6.63849i) q^{5} +(25.9322 - 7.51816i) q^{9} +(1.13857 + 0.657354i) q^{11} -23.9754i q^{13} +(24.5683 + 31.3513i) q^{15} +(29.5490 - 51.1804i) q^{17} +(24.4639 - 14.1243i) q^{19} +(65.7234 - 37.9454i) q^{23} +(33.1203 - 57.3661i) q^{25} +(127.915 - 57.6258i) q^{27} +302.001i q^{29} +(80.9549 + 46.7393i) q^{31} +(6.33773 + 2.54982i) q^{33} +(-133.433 - 231.113i) q^{37} +(-17.5187 - 123.342i) q^{39} +142.471 q^{41} +284.654 q^{43} +(149.300 + 143.335i) q^{45} +(104.876 + 181.651i) q^{47} +(114.618 - 284.890i) q^{51} +(545.190 + 314.765i) q^{53} +10.0779i q^{55} +(115.535 - 90.5383i) q^{57} +(-365.186 + 632.521i) q^{59} +(-471.964 + 272.488i) q^{61} +(159.160 - 91.8912i) q^{65} +(240.556 - 416.655i) q^{67} +(310.389 - 243.235i) q^{69} -46.5477i q^{71} +(834.095 + 481.565i) q^{73} +(128.471 - 319.322i) q^{75} +(-630.818 - 1092.61i) q^{79} +(615.955 - 389.924i) q^{81} -841.130 q^{83} +453.014 q^{85} +(220.671 + 1553.65i) q^{87} +(-641.169 - 1110.54i) q^{89} +(450.626 + 181.298i) q^{93} +(187.528 + 108.269i) q^{95} +60.2806i q^{97} +(34.4677 + 8.48666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 64 q^{9}+O(q^{10}) $ 48 * q + 64 * q^9	$ 48 q + 64 q^{9} - 192 q^{15} - 456 q^{25} + 432 q^{37} - 688 q^{39} + 1248 q^{43} + 1536 q^{51} - 2720 q^{57} + 528 q^{67} - 3744 q^{79} - 3408 q^{81} + 13824 q^{85} + 5088 q^{93} - 15472 q^{99}+O(q^{100}) $ 48 * q + 64 * q^9 - 192 * q^15 - 456 * q^25 + 432 * q^37 - 688 * q^39 + 1248 * q^43 + 1536 * q^51 - 2720 * q^57 + 528 * q^67 - 3744 * q^79 - 3408 * q^81 + 13824 * q^85 + 5088 * q^93 - 15472 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	5.14452	−	0.730696i	0.990063	−	0.140622i
$3$	5.14452	−	0.730696i	0.990063	−	0.140622i
$4$		0			0
$5$	3.83273	+	6.63849i	0.342810	+	0.593764i	0.984953	−	0.172820i	$-0.0552879\pi$
$5$	3.83273	+	6.63849i	0.342810	+	0.593764i	−0.642143	+	0.766585i	$0.721955\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	25.9322	−	7.51816i	0.960451	−	0.278450i
$10$		0			0
$11$	1.13857	+	0.657354i	0.0312084	+	0.0180182i	0.515523	−	0.856876i	$-0.327598\pi$
$11$	1.13857	+	0.657354i	0.0312084	+	0.0180182i	−0.484315	+	0.874894i	$0.660931\pi$
$12$		0			0
$13$		−	23.9754i		−	0.511505i	−0.966742	−	0.255753i	$-0.917677\pi$
$13$		−	23.9754i		−	0.511505i	0.966742	−	0.255753i	$-0.0823233\pi$
$14$		0			0
$15$	24.5683	+	31.3513i	0.422900	+	0.539658i
$16$		0			0
$17$	29.5490	−	51.1804i	0.421570	−	0.730181i	−0.574523	−	0.818488i	$-0.694813\pi$
$17$	29.5490	−	51.1804i	0.421570	−	0.730181i	0.996093	+	0.0883076i	$0.0281458\pi$
$18$		0			0
$19$	24.4639	−	14.1243i	0.295390	−	0.170544i	−0.344980	−	0.938610i	$-0.612114\pi$
$19$	24.4639	−	14.1243i	0.295390	−	0.170544i	0.640370	+	0.768066i	$0.278781\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	65.7234	−	37.9454i	0.595838	−	0.344008i	−0.171564	−	0.985173i	$-0.554882\pi$
$23$	65.7234	−	37.9454i	0.595838	−	0.344008i	0.767403	+	0.641165i	$0.221549\pi$
$24$		0			0
$25$	33.1203	−	57.3661i	0.264963	−	0.458929i
$26$		0			0
$27$	127.915	−	57.6258i	0.911751	−	0.410744i
$28$		0			0
$29$			302.001i			1.93380i	0.255151	+	0.966901i	$0.417875\pi$
$29$			302.001i			1.93380i	−0.255151	+	0.966901i	$0.582125\pi$
$30$		0			0
$31$	80.9549	+	46.7393i	0.469030	+	0.270795i	0.715834	−	0.698271i	$-0.246047\pi$
$31$	80.9549	+	46.7393i	0.469030	+	0.270795i	−0.246804	+	0.969066i	$0.579380\pi$
$32$		0			0
$33$	6.33773	+	2.54982i	0.0334320	+	0.0134505i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−133.433	−	231.113i	−0.592871	−	1.02688i	−0.993843	−	0.110793i	$-0.964661\pi$
$37$	−133.433	−	231.113i	−0.592871	−	1.02688i	0.400972	−	0.916090i	$-0.368672\pi$
$38$		0			0
$39$	−17.5187	−	123.342i	−0.0719292	−	0.506423i
$40$		0			0
$41$	142.471			0.542688			0.271344	−	0.962482i	$-0.412532\pi$
$41$	142.471			0.542688			0.271344	+	0.962482i	$0.412532\pi$
$42$		0			0
$43$	284.654			1.00952			0.504760	−	0.863260i	$-0.331581\pi$
$43$	284.654			1.00952			0.504760	+	0.863260i	$0.331581\pi$
$44$		0			0
$45$	149.300	+	143.335i	0.494586	+	0.474826i
$46$		0			0
$47$	104.876	+	181.651i	0.325484	+	0.563755i	0.981610	−	0.190896i	$-0.0611393\pi$
$47$	104.876	+	181.651i	0.325484	+	0.563755i	−0.656126	+	0.754651i	$0.727806\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	114.618	−	284.890i	0.314701	−	0.782207i
$52$		0			0
$53$	545.190	+	314.765i	1.41297	+	0.815780i	0.995667	−	0.0929859i	$-0.0296412\pi$
$53$	545.190	+	314.765i	1.41297	+	0.815780i	0.417306	+	0.908766i	$0.362974\pi$
$54$		0			0
$55$			10.0779i			0.0247072i
$56$		0			0
$57$	115.535	−	90.5383i	0.268473	−	0.210387i
$58$		0			0
$59$	−365.186	+	632.521i	−0.805817	+	1.39572i	0.109922	+	0.993940i	$0.464940\pi$
$59$	−365.186	+	632.521i	−0.805817	+	1.39572i	−0.915738	+	0.401775i	$0.868393\pi$
$60$		0			0
$61$	−471.964	+	272.488i	−0.990635	+	0.571943i	−0.905464	−	0.424423i	$-0.860477\pi$
$61$	−471.964	+	272.488i	−0.990635	+	0.571943i	−0.0851710	+	0.996366i	$0.527144\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	159.160	−	91.8912i	0.303714	−	0.175349i
$66$		0			0
$67$	240.556	−	416.655i	0.438635	−	0.759739i	−0.558949	−	0.829202i	$-0.688795\pi$
$67$	240.556	−	416.655i	0.438635	−	0.759739i	0.997585	+	0.0694632i	$0.0221286\pi$
$68$		0			0
$69$	310.389	−	243.235i	0.541543	−	0.424377i
$70$		0			0
$71$		−	46.5477i		−	0.0778056i	−0.999243	−	0.0389028i	$-0.987614\pi$
$71$		−	46.5477i		−	0.0778056i	0.999243	−	0.0389028i	$-0.0123863\pi$
$72$		0			0
$73$	834.095	+	481.565i	1.33731	+	0.772095i	0.986407	−	0.164318i	$-0.0525423\pi$
$73$	834.095	+	481.565i	1.33731	+	0.772095i	0.350900	+	0.936413i	$0.385876\pi$
$74$		0			0
$75$	128.471	−	319.322i	0.197794	−	0.491628i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−630.818	−	1092.61i	−0.898386	−	1.55605i	−0.829557	−	0.558422i	$-0.811407\pi$
$79$	−630.818	−	1092.61i	−0.898386	−	1.55605i	−0.0688294	−	0.997628i	$-0.521926\pi$
$80$		0			0
$81$	615.955	−	389.924i	0.844931	−	0.534876i
$82$		0			0
$83$	−841.130			−1.11236			−0.556181	−	0.831061i	$-0.687734\pi$
$83$	−841.130			−1.11236			−0.556181	+	0.831061i	$0.687734\pi$
$84$		0			0
$85$	453.014			0.578074
$86$		0			0
$87$	220.671	+	1553.65i	0.271936	+	1.91459i
$88$		0			0
$89$	−641.169	−	1110.54i	−0.763638	−	1.32266i	−0.940964	−	0.338507i	$-0.890078\pi$
$89$	−641.169	−	1110.54i	−0.763638	−	1.32266i	0.177326	−	0.984152i	$-0.443255\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	450.626	+	181.298i	0.502449	+	0.202148i
$94$		0			0
$95$	187.528	+	108.269i	0.202525	+	0.116928i
$96$		0			0
$97$			60.2806i			0.0630986i	0.999502	+	0.0315493i	$0.0100441\pi$
$97$			60.2806i			0.0630986i	−0.999502	+	0.0315493i	$0.989956\pi$
$98$		0			0
$99$	34.4677	+	8.48666i	0.0349913	+	0.00861557i
$100$		0			0
$101$	−584.358	+	1012.14i	−0.575701	+	0.997144i	0.420264	+	0.907402i	$0.361938\pi$
$101$	−584.358	+	1012.14i	−0.575701	+	0.997144i	−0.995965	+	0.0897419i	$0.971396\pi$
$102$		0			0
$103$	15.8686	−	9.16173i	0.0151804	−	0.00876439i	−0.492391	−	0.870374i	$-0.663877\pi$
$103$	15.8686	−	9.16173i	0.0151804	−	0.00876439i	0.507571	+	0.861610i	$0.330544\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	824.968	−	476.295i	0.745352	−	0.430329i	−0.0786602	−	0.996901i	$-0.525064\pi$
$107$	824.968	−	476.295i	0.745352	−	0.430329i	0.824012	+	0.566572i	$0.191731\pi$
$108$		0			0
$109$	353.940	−	613.042i	0.311021	−	0.538704i	−0.667563	−	0.744554i	$-0.732662\pi$
$109$	353.940	−	613.042i	0.311021	−	0.538704i	0.978584	+	0.205849i	$0.0659957\pi$
$110$		0			0
$111$	−855.322	−	1091.46i	−0.731383	−	0.933309i
$112$		0			0
$113$			9.01287i			0.00750318i	0.999993	+	0.00375159i	$0.00119417\pi$
$113$			9.01287i			0.00750318i	−0.999993	+	0.00375159i	$0.998806\pi$
$114$		0			0
$115$	503.801	+	290.870i	0.408519	+	0.235858i
$116$		0			0
$117$	−180.251	−	621.733i	−0.142429	−	0.491276i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−664.636	−	1151.18i	−0.499351	−	0.864901i
$122$		0			0
$123$	732.944	−	104.103i	0.537296	−	0.0763141i
$124$		0			0
$125$	1465.95			1.04895
$126$		0			0
$127$	387.174			0.270521			0.135260	−	0.990810i	$-0.456813\pi$
$127$	387.174			0.270521			0.135260	+	0.990810i	$0.456813\pi$
$128$		0			0
$129$	1464.41	−	207.996i	0.999488	−	0.141961i
$130$		0			0
$131$	705.778	+	1222.44i	0.470718	+	0.815308i	0.999439	−	0.0334876i	$-0.0106614\pi$
$131$	705.778	+	1222.44i	0.470718	+	0.815308i	−0.528721	+	0.848796i	$0.677328\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	872.813	+	628.298i	0.556443	+	0.400558i
$136$		0			0
$137$	631.197	+	364.422i	0.393626	+	0.227260i	0.683730	−	0.729735i	$-0.260357\pi$
$137$	631.197	+	364.422i	0.393626	+	0.227260i	−0.290104	+	0.956995i	$0.593690\pi$
$138$		0			0
$139$			1262.40i			0.770324i	0.922849	+	0.385162i	$0.125854\pi$
$139$			1262.40i			0.770324i	−0.922849	+	0.385162i	$0.874146\pi$
$140$		0			0
$141$	672.269	+	857.874i	0.401527	+	0.512383i
$142$		0			0
$143$	15.7603	−	27.2977i	0.00921639	−	0.0159632i
$144$		0			0
$145$	−2004.83	+	1157.49i	−1.14822	+	0.662927i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	817.509	−	471.989i	0.449483	−	0.259509i	−0.258129	−	0.966111i	$-0.583106\pi$
$149$	817.509	−	471.989i	0.449483	−	0.259509i	0.707612	+	0.706601i	$0.249773\pi$
$150$		0			0
$151$	−153.771	+	266.339i	−0.0828722	+	0.143539i	−0.904483	−	0.426511i	$-0.859743\pi$
$151$	−153.771	+	266.339i	−0.0828722	+	0.143539i	0.821610	+	0.570050i	$0.193076\pi$
$152$		0			0
$153$	381.488	−	1549.37i	0.201578	−	0.818689i
$154$		0			0
$155$			716.557i			0.371324i
$156$		0			0
$157$	−1614.46	−	932.111i	−0.820690	−	0.473825i	0.0299645	−	0.999551i	$-0.490461\pi$
$157$	−1614.46	−	932.111i	−0.820690	−	0.473825i	−0.850654	+	0.525726i	$0.823794\pi$
$158$		0			0
$159$	3034.74	+	1220.95i	1.51365	+	0.608978i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1620.61	−	2806.98i	−0.778749	−	1.34883i	−0.932663	−	0.360749i	$-0.882521\pi$
$163$	−1620.61	−	2806.98i	−0.778749	−	1.34883i	0.153913	−	0.988084i	$-0.450812\pi$
$164$		0			0
$165$	7.36384	+	51.8457i	0.00347439	+	0.0244617i
$166$		0			0
$167$	2021.13			0.936523			0.468262	−	0.883590i	$-0.344881\pi$
$167$	2021.13			0.936523			0.468262	+	0.883590i	$0.344881\pi$
$168$		0			0
$169$	1622.18			0.738362
$170$		0			0
$171$	528.215	−	550.197i	0.236220	−	0.246050i
$172$		0			0
$173$	−350.294	−	606.727i	−0.153944	−	0.266639i	0.778730	−	0.627359i	$-0.215864\pi$
$173$	−350.294	−	606.727i	−0.153944	−	0.266639i	−0.932674	+	0.360720i	$0.882531\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1416.53	+	3520.86i	−0.601541	+	1.49516i
$178$		0			0
$179$	−2484.84	−	1434.62i	−1.03757	−	0.599043i	−0.118428	−	0.992963i	$-0.537785\pi$
$179$	−2484.84	−	1434.62i	−1.03757	−	0.599043i	−0.919145	+	0.393920i	$0.871119\pi$
$180$		0			0
$181$			1974.33i			0.810778i	0.914144	+	0.405389i	$0.132864\pi$
$181$			1974.33i			0.810778i	−0.914144	+	0.405389i	$0.867136\pi$
$182$		0			0
$183$	−2228.92	+	1746.68i	−0.900363	+	0.705566i
$184$		0			0
$185$	1022.83	−	1771.59i	0.406485	−	0.704052i
$186$		0			0
$187$	67.2873	−	38.8483i	0.0263130	−	0.0151918i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−941.978	+	543.851i	−0.356854	+	0.206030i	−0.667700	−	0.744431i	$-0.732721\pi$
$191$	−941.978	+	543.851i	−0.356854	+	0.206030i	0.310846	+	0.950460i	$0.399388\pi$
$192$		0			0
$193$	−1917.52	+	3321.24i	−0.715161	+	1.23870i	0.247736	+	0.968828i	$0.420314\pi$
$193$	−1917.52	+	3321.24i	−0.715161	+	1.23870i	−0.962897	+	0.269868i	$0.913020\pi$
$194$		0			0
$195$	751.658	−	589.034i	0.276038	−	0.216316i
$196$		0			0
$197$			1635.24i			0.591400i	0.955281	+	0.295700i	$0.0955528\pi$
$197$			1635.24i			0.591400i	−0.955281	+	0.295700i	$0.904447\pi$
$198$		0			0
$199$	−3734.89	−	2156.34i	−1.33045	−	0.768134i	−0.345079	−	0.938574i	$-0.612148\pi$
$199$	−3734.89	−	2156.34i	−1.33045	−	0.768134i	−0.985368	+	0.170439i	$0.945481\pi$
$200$		0			0
$201$	933.096	−	2319.26i	0.327440	−	0.813871i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	546.053	+	945.791i	0.186039	+	0.322229i
$206$		0			0
$207$	1419.07	−	1478.13i	0.476484	−	0.496314i
$208$		0			0
$209$	37.1386			0.0122915
$210$		0			0
$211$	−2882.49			−0.940468			−0.470234	−	0.882542i	$-0.655831\pi$
$211$	−2882.49			−0.940468			−0.470234	+	0.882542i	$0.655831\pi$
$212$		0			0
$213$	−34.0122	−	239.466i	−0.0109412	−	0.0770325i
$214$		0			0
$215$	1091.00	+	1889.67i	0.346073	+	0.599417i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	4642.90	+	1867.95i	1.43259	+	0.576367i
$220$		0			0
$221$	−1227.07	−	708.449i	−0.373491	−	0.215635i
$222$		0			0
$223$			3378.49i			1.01453i	0.861790	+	0.507265i	$0.169344\pi$
$223$			3378.49i			1.01453i	−0.861790	+	0.507265i	$0.830656\pi$
$224$		0			0
$225$	427.594	−	1736.63i	0.126695	−	0.514557i
$226$		0			0
$227$	2538.84	−	4397.39i	0.742328	−	1.28575i	−0.209105	−	0.977893i	$-0.567055\pi$
$227$	2538.84	−	4397.39i	0.742328	−	1.28575i	0.951433	−	0.307857i	$-0.0996117\pi$
$228$		0			0
$229$	−3784.94	+	2185.24i	−1.09221	+	0.630587i	−0.934164	−	0.356844i	$-0.883853\pi$
$229$	−3784.94	+	2185.24i	−1.09221	+	0.630587i	−0.158046	+	0.987432i	$0.550519\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3335.56	+	1925.79i	−0.937854	+	0.541470i	−0.889287	−	0.457350i	$-0.848799\pi$
$233$	−3335.56	+	1925.79i	−0.937854	+	0.541470i	−0.0485671	+	0.998820i	$0.515465\pi$
$234$		0			0
$235$	−803.925	+	1392.44i	−0.223159	+	0.386522i
$236$		0			0
$237$	−4043.62	−	5160.01i	−1.10827	−	1.41426i
$238$		0			0
$239$		−	7067.79i		−	1.91288i	−0.291937	−	0.956438i	$-0.594300\pi$
$239$		−	7067.79i		−	1.91288i	0.291937	−	0.956438i	$-0.405700\pi$
$240$		0			0
$241$	−2636.64	−	1522.26i	−0.704733	−	0.406878i	0.104375	−	0.994538i	$-0.466716\pi$
$241$	−2636.64	−	1522.26i	−0.704733	−	0.406878i	−0.809108	+	0.587660i	$0.800049\pi$
$242$		0			0
$243$	2883.87	−	2456.05i	0.761319	−	0.648377i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−338.634	−	586.532i	−0.0872340	−	0.151094i
$248$		0			0
$249$	−4327.21	+	614.610i	−1.10131	+	0.156423i
$250$		0			0
$251$	−5439.29			−1.36783			−0.683914	−	0.729562i	$-0.739724\pi$
$251$	−5439.29			−1.36783			−0.683914	+	0.729562i	$0.739724\pi$
$252$		0			0
$253$	99.7744			0.0247935
$254$		0			0
$255$	2330.54	−	331.015i	0.572330	−	0.0812902i
$256$		0			0
$257$	−1139.37	−	1973.45i	−0.276545	−	0.478990i	0.693979	−	0.719996i	$-0.255856\pi$
$257$	−1139.37	−	1973.45i	−0.276545	−	0.478990i	−0.970524	+	0.241005i	$0.922523\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	2270.50	+	7831.55i	0.538468	+	1.85732i
$262$		0			0
$263$	1003.97	+	579.643i	0.235390	+	0.135902i	0.613056	−	0.790039i	$-0.289940\pi$
$263$	1003.97	+	579.643i	0.235390	+	0.135902i	−0.377666	+	0.925942i	$0.623273\pi$
$264$		0			0
$265$			4825.65i			1.11863i
$266$		0			0
$267$	−4109.97	−	5244.68i	−0.942045	−	1.20213i
$268$		0			0
$269$	−1873.94	+	3245.77i	−0.424745	+	0.735680i	−0.996397	−	0.0848164i	$-0.972970\pi$
$269$	−1873.94	+	3245.77i	−0.424745	+	0.735680i	0.571651	+	0.820497i	$0.306303\pi$
$270$		0			0
$271$	1771.74	−	1022.91i	0.397142	−	0.229290i	−0.288108	−	0.957598i	$-0.593026\pi$
$271$	1771.74	−	1022.91i	0.397142	−	0.229290i	0.685250	+	0.728308i	$0.259693\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	75.4197	−	43.5436i	0.0165381	−	0.00954827i
$276$		0			0
$277$	−2421.58	+	4194.29i	−0.525265	+	0.909785i	0.474302	+	0.880362i	$0.342700\pi$
$277$	−2421.58	+	4194.29i	−0.525265	+	0.909785i	−0.999567	+	0.0294232i	$0.990633\pi$
$278$		0			0
$279$	2450.73	+	603.420i	0.525883	+	0.129483i
$280$		0			0
$281$		−	827.961i		−	0.175772i	−0.996131	−	0.0878862i	$-0.971989\pi$
$281$		−	827.961i		−	0.175772i	0.996131	−	0.0878862i	$-0.0280112\pi$
$282$		0			0
$283$	−7402.44	−	4273.80i	−1.55487	−	0.897707i	−0.997734	−	0.0672878i	$-0.978565\pi$
$283$	−7402.44	−	4273.80i	−1.55487	−	0.897707i	−0.557140	−	0.830419i	$-0.688101\pi$
$284$		0			0
$285$	1043.85	+	419.967i	0.216956	+	0.0872866i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	710.211	+	1230.12i	0.144557	+	0.250381i
$290$		0			0
$291$	44.0468	+	310.115i	0.00887308	+	0.0624716i
$292$		0			0
$293$	−7266.94			−1.44894			−0.724469	−	0.689307i	$-0.757915\pi$
$293$	−7266.94			−1.44894			−0.724469	+	0.689307i	$0.757915\pi$
$294$		0			0
$295$	−5598.64			−1.10497
$296$		0			0
$297$	183.521	+	18.4744i	0.0358551	+	0.00360940i
$298$		0			0
$299$	−909.756	−	1575.74i	−0.175962	−	0.304775i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−2266.68	+	5633.95i	−0.429760	+	1.06819i
$304$		0			0
$305$	−3617.82	−	2088.75i	−0.679199	−	0.392136i
$306$		0			0
$307$			4124.73i			0.766811i	0.923580	+	0.383406i	$0.125249\pi$
$307$			4124.73i			0.766811i	−0.923580	+	0.383406i	$0.874751\pi$
$308$		0			0
$309$	74.9418	−	58.7278i	0.0137971	−	0.0108120i
$310$		0			0
$311$	1649.15	−	2856.41i	0.300691	−	0.520812i	−0.675602	−	0.737267i	$-0.736116\pi$
$311$	1649.15	−	2856.41i	0.300691	−	0.520812i	0.976293	+	0.216455i	$0.0694495\pi$
$312$		0			0
$313$	−5188.30	+	2995.47i	−0.936934	+	0.540939i	−0.888998	−	0.457912i	$-0.848598\pi$
$313$	−5188.30	+	2995.47i	−0.936934	+	0.540939i	−0.0479358	+	0.998850i	$0.515264\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6144.35	+	3547.44i	−1.08865	+	0.628531i	−0.933216	−	0.359316i	$-0.883010\pi$
$317$	−6144.35	+	3547.44i	−1.08865	+	0.628531i	−0.155432	+	0.987847i	$0.549677\pi$
$318$		0			0
$319$	−198.522	+	343.850i	−0.0348436	+	0.0603508i
$320$		0			0
$321$	3896.04	−	3053.11i	0.677431	−	0.530866i
$322$		0			0
$323$		−	1669.43i		−	0.287584i
$324$		0			0
$325$	−1375.37	−	794.072i	−0.234744	−	0.135530i
$326$		0			0
$327$	1372.90	−	3412.43i	0.232177	−	0.577088i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−4581.91	−	7936.10i	−0.760860	−	1.31785i	−0.942408	−	0.334466i	$-0.891444\pi$
$331$	−4581.91	−	7936.10i	−0.760860	−	1.31785i	0.181548	−	0.983382i	$-0.441889\pi$
$332$		0			0
$333$	−5197.75	−	4990.08i	−0.855360	−	0.821186i
$334$		0			0
$335$	3687.94			0.601474
$336$		0			0
$337$	1546.78			0.250025			0.125012	−	0.992155i	$-0.460103\pi$
$337$	1546.78			0.250025			0.125012	+	0.992155i	$0.460103\pi$
$338$		0			0
$339$	6.58567	+	46.3669i	0.00105512	+	0.00742862i
$340$		0			0
$341$	61.4486	+	106.432i	0.00975844	+	0.0169021i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2804.35	+	1128.26i	0.437627	+	0.176068i
$346$		0			0
$347$	7966.18	+	4599.27i	1.23241	+	0.711533i	0.967532	−	0.252749i	$-0.0813346\pi$
$347$	7966.18	+	4599.27i	1.23241	+	0.711533i	0.264879	+	0.964282i	$0.414668\pi$
$348$		0			0
$349$			6916.38i			1.06082i	0.847742	+	0.530409i	$0.177962\pi$
$349$			6916.38i			1.06082i	−0.847742	+	0.530409i	$0.822038\pi$
$350$		0			0
$351$	−1381.60	−	3066.81i	−0.210098	−	0.466365i
$352$		0			0
$353$	−1376.71	+	2384.52i	−0.207577	+	0.359534i	−0.950951	−	0.309343i	$-0.899891\pi$
$353$	−1376.71	+	2384.52i	−0.207577	+	0.359534i	0.743374	+	0.668876i	$0.233224\pi$
$354$		0			0
$355$	309.007	−	178.405i	0.0461982	−	0.0266725i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3079.84	+	1778.15i	−0.452780	+	0.261413i	−0.709004	−	0.705205i	$-0.750855\pi$
$359$	−3079.84	+	1778.15i	−0.452780	+	0.261413i	0.256224	+	0.966618i	$0.417522\pi$
$360$		0			0
$361$	−3030.51	+	5249.00i	−0.441830	+	0.765272i
$362$		0			0
$363$	−4260.40	−	5436.64i	−0.616013	−	0.786087i
$364$		0			0
$365$			7382.84i			1.05873i
$366$		0			0
$367$	−4788.83	−	2764.83i	−0.681131	−	0.393251i	0.119150	−	0.992876i	$-0.461983\pi$
$367$	−4788.83	−	2764.83i	−0.681131	−	0.393251i	−0.800281	+	0.599625i	$0.795316\pi$
$368$		0			0
$369$	3694.58	−	1071.12i	0.521225	−	0.151112i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	566.970	+	982.020i	0.0787039	+	0.136319i	0.902691	−	0.430289i	$-0.141588\pi$
$373$	566.970	+	982.020i	0.0787039	+	0.136319i	−0.823987	+	0.566609i	$0.808255\pi$
$374$		0			0
$375$	7541.60	−	1071.16i	1.03852	−	0.147506i
$376$		0			0
$377$	7240.60			0.989150
$378$		0			0
$379$	4071.36			0.551799			0.275900	−	0.961186i	$-0.411024\pi$
$379$	4071.36			0.551799			0.275900	+	0.961186i	$0.411024\pi$
$380$		0			0
$381$	1991.82	−	282.906i	0.267833	−	0.0380413i
$382$		0			0
$383$	7069.27	+	12244.3i	0.943140	+	1.63357i	0.759433	+	0.650586i	$0.225477\pi$
$383$	7069.27	+	12244.3i	0.943140	+	1.63357i	0.183707	+	0.982981i	$0.441190\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7381.70	−	2140.07i	0.969594	−	0.281101i
$388$		0			0
$389$	−9257.16	−	5344.63i	−1.20657	−	0.696615i	−0.244564	−	0.969633i	$-0.578645\pi$
$389$	−9257.16	−	5344.63i	−1.20657	−	0.696615i	−0.962009	+	0.273018i	$0.911978\pi$
$390$		0			0
$391$		−	4485.00i		−	0.580093i
$392$		0			0
$393$	4524.12	+	5773.18i	0.580692	+	0.741013i
$394$		0			0
$395$	4835.51	−	8375.35i	0.615952	−	1.06686i
$396$		0			0
$397$	−8778.93	+	5068.52i	−1.10983	+	0.640760i	−0.938785	−	0.344504i	$-0.888047\pi$
$397$	−8778.93	+	5068.52i	−1.10983	+	0.640760i	−0.171043	+	0.985263i	$0.554714\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7292.21	−	4210.16i	0.908119	−	0.524303i	0.0282934	−	0.999600i	$-0.490993\pi$
$401$	7292.21	−	4210.16i	0.908119	−	0.524303i	0.879825	+	0.475297i	$0.157659\pi$
$402$		0			0
$403$	1120.59	−	1940.92i	0.138513	−	0.239911i
$404$		0			0
$405$	4949.30	+	2594.53i	0.607241	+	0.318329i
$406$		0			0
$407$		−	350.851i		−	0.0427298i
$408$		0			0
$409$	8021.64	+	4631.30i	0.969792	+	0.559909i	0.899173	−	0.437594i	$-0.144169\pi$
$409$	8021.64	+	4631.30i	0.969792	+	0.559909i	0.0706189	+	0.997503i	$0.477503\pi$
$410$		0			0
$411$	3513.49	+	1413.56i	0.421673	+	0.169649i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−3223.83	−	5583.83i	−0.381329	−	0.660480i
$416$		0			0
$417$	922.428	+	6494.42i	0.108325	+	0.762670i
$418$		0			0
$419$	−883.038			−0.102958			−0.0514788	−	0.998674i	$-0.516393\pi$
$419$	−883.038			−0.102958			−0.0514788	+	0.998674i	$0.516393\pi$
$420$		0			0
$421$	6313.53			0.730886			0.365443	−	0.930834i	$-0.380918\pi$
$421$	6313.53			0.730886			0.365443	+	0.930834i	$0.380918\pi$
$422$		0			0
$423$	4085.35	+	3922.12i	0.469589	+	0.450828i
$424$		0			0
$425$	−1957.35	−	3390.22i	−0.223401	−	0.386941i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	61.1329	−	151.949i	0.00688001	−	0.0171007i
$430$		0			0
$431$	6291.22	+	3632.24i	0.703103	+	0.405937i	0.808502	−	0.588493i	$-0.200279\pi$
$431$	6291.22	+	3632.24i	0.703103	+	0.405937i	−0.105399	+	0.994430i	$0.533612\pi$
$432$		0			0
$433$		−	4242.72i		−	0.470883i	−0.971889	−	0.235441i	$-0.924346\pi$
$433$		−	4242.72i		−	0.470883i	0.971889	−	0.235441i	$-0.0756536\pi$
$434$		0			0
$435$	−9468.13	+	7419.66i	−1.04359	+	0.817806i
$436$		0			0
$437$	1071.90	−	1856.59i	0.117337	−	0.203233i
$438$		0			0
$439$	9430.55	−	5444.73i	1.02528	−	0.591943i	0.109648	−	0.993971i	$-0.465028\pi$
$439$	9430.55	−	5444.73i	1.02528	−	0.591943i	0.915628	+	0.402028i	$0.131694\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	13925.6	−	8039.92i	1.49351	−	0.862276i	0.493534	−	0.869727i	$-0.335705\pi$
$443$	13925.6	−	8039.92i	1.49351	−	0.862276i	0.999972	+	0.00745048i	$0.00237158\pi$
$444$		0			0
$445$	4914.86	−	8512.78i	0.523565	−	0.906842i
$446$		0			0
$447$	3860.81	−	3025.51i	0.408524	−	0.320138i
$448$		0			0
$449$			13638.3i			1.43348i	0.697341	+	0.716740i	$0.254366\pi$
$449$			13638.3i			1.43348i	−0.697341	+	0.716740i	$0.745634\pi$
$450$		0			0
$451$	162.213	+	93.6538i	0.0169364	+	0.00977824i
$452$		0			0
$453$	−596.465	+	1482.55i	−0.0618640	+	0.153766i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−939.399	−	1627.09i	−0.0961559	−	0.166547i	0.813935	−	0.580957i	$-0.197321\pi$
$457$	−939.399	−	1627.09i	−0.0961559	−	0.166547i	−0.910090	+	0.414410i	$0.863988\pi$
$458$		0			0
$459$	830.451	−	8249.53i	0.0844490	−	0.838900i
$460$		0			0
$461$	2579.48			0.260604			0.130302	−	0.991474i	$-0.458405\pi$
$461$	2579.48			0.260604			0.130302	+	0.991474i	$0.458405\pi$
$462$		0			0
$463$	6099.88			0.612280			0.306140	−	0.951986i	$-0.400962\pi$
$463$	6099.88			0.612280			0.306140	+	0.951986i	$0.400962\pi$
$464$		0			0
$465$	523.585	+	3686.34i	0.0522165	+	0.367635i
$466$		0			0
$467$	−9526.74	−	16500.8i	−0.943993	−	1.63504i	−0.757755	−	0.652540i	$-0.773704\pi$
$467$	−9526.74	−	16500.8i	−0.943993	−	1.63504i	−0.186239	−	0.982505i	$-0.559630\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−8986.73	−	3615.58i	−0.879165	−	0.353710i
$472$		0			0
$473$	324.099	+	187.119i	0.0315054	+	0.0181897i
$474$		0			0
$475$		−	1871.20i		−	0.180751i
$476$		0			0
$477$	16504.4	+	4063.73i	1.58425	+	0.390074i
$478$		0			0
$479$	−8990.07	+	15571.3i	−0.857551	+	1.48532i	0.0167077	+	0.999860i	$0.494682\pi$
$479$	−8990.07	+	15571.3i	−0.857551	+	1.48532i	−0.874258	+	0.485461i	$0.838652\pi$
$480$		0			0
$481$	−5541.01	+	3199.10i	−0.525256	+	0.303257i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−400.172	+	231.039i	−0.0374657	+	0.0216308i
$486$		0			0
$487$	6157.30	−	10664.8i	0.572924	−	0.992333i	−0.423340	−	0.905971i	$-0.639142\pi$
$487$	6157.30	−	10664.8i	0.572924	−	0.992333i	0.996264	−	0.0863623i	$-0.0275243\pi$
$488$		0			0
$489$	−10388.3	−	13256.4i	−0.960688	−	1.22592i
$490$		0			0
$491$		−	6650.90i		−	0.611305i	−0.952143	−	0.305653i	$-0.901125\pi$
$491$		−	6650.90i		−	0.611305i	0.952143	−	0.305653i	$-0.0988747\pi$
$492$		0			0
$493$	15456.6	+	8923.85i	1.41203	+	0.815233i
$494$		0			0
$495$	75.7669	+	261.341i	0.00687973	+	0.0237301i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−6376.49	−	11044.4i	−0.572046	−	0.990813i	−0.996356	−	0.0852957i	$-0.972816\pi$
$499$	−6376.49	−	11044.4i	−0.572046	−	0.990813i	0.424310	−	0.905517i	$-0.360517\pi$
$500$		0			0
$501$	10397.7	−	1476.83i	0.927217	−	0.131696i
$502$		0			0
$503$	7044.47			0.624448			0.312224	−	0.950009i	$-0.398926\pi$
$503$	7044.47			0.624448			0.312224	+	0.950009i	$0.398926\pi$
$504$		0			0
$505$	−8958.76			−0.789425
$506$		0			0
$507$	8345.35	−	1185.32i	0.731025	−	0.103830i
$508$		0			0
$509$	2386.47	+	4133.49i	0.207816	+	0.359948i	0.951026	−	0.309110i	$-0.100031\pi$
$509$	2386.47	+	4133.49i	0.207816	+	0.359948i	−0.743210	+	0.669058i	$0.766698\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	2315.38	−	3216.46i	0.199272	−	0.276823i
$514$		0			0
$515$	121.640	+	70.2289i	0.0104080	+	0.00600904i
$516$		0			0
$517$			275.763i			0.0234585i
$518$		0			0
$519$	−2245.43	−	2865.36i	−0.189910	−	0.242342i
$520$		0			0
$521$	−7491.53	+	12975.7i	−0.629961	+	1.09113i	0.357597	+	0.933876i	$0.383596\pi$
$521$	−7491.53	+	12975.7i	−0.629961	+	1.09113i	−0.987559	+	0.157249i	$0.949737\pi$
$522$		0			0
$523$	4638.56	−	2678.07i	0.387820	−	0.223908i	−0.293395	−	0.955991i	$-0.594785\pi$
$523$	4638.56	−	2678.07i	0.387820	−	0.223908i	0.681215	+	0.732083i	$0.261452\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4784.27	−	2762.20i	0.395458	−	0.228318i
$528$		0			0
$529$	−3203.79	+	5549.12i	−0.263318	+	0.456080i
$530$		0			0
$531$	−4714.68	+	19148.2i	−0.385310	+	1.56490i
$532$		0			0
$533$		−	3415.79i		−	0.277588i
$534$		0			0
$535$	6323.76	+	3651.03i	0.511028	+	0.295042i
$536$		0			0
$537$	−13831.6	−	5564.78i	−1.11150	−	0.447184i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.18626	+	7.25082i	0.000332683	+	0.000576224i	0.866192	−	0.499712i	$-0.166561\pi$
$541$	4.18626	+	7.25082i	0.000332683	+	0.000576224i	−0.865859	+	0.500288i	$0.833227\pi$
$542$		0			0
$543$	1442.63	+	10157.0i	0.114014	+	0.802721i
$544$		0			0
$545$	5426.23			0.426485
$546$		0			0
$547$	10274.7			0.803137			0.401568	−	0.915829i	$-0.368465\pi$
$547$	10274.7			0.803137			0.401568	+	0.915829i	$0.368465\pi$
$548$		0			0
$549$	−10190.4	+	10614.5i	−0.792198	+	0.825166i
$550$		0			0
$551$	4265.55	+	7388.15i	0.329798	+	0.571226i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3967.46	−	9861.33i	0.303440	−	0.754217i
$556$		0			0
$557$	13316.1	+	7688.05i	1.01296	+	0.584835i	0.912058	−	0.410061i	$-0.134493\pi$
$557$	13316.1	+	7688.05i	1.01296	+	0.584835i	0.100906	+	0.994896i	$0.467826\pi$
$558$		0			0
$559$		−	6824.68i		−	0.516375i
$560$		0			0
$561$	317.775	−	249.023i	0.0239152	−	0.0187411i
$562$		0			0
$563$	−9229.97	+	15986.8i	−0.690936	+	1.19674i	0.280596	+	0.959826i	$0.409468\pi$
$563$	−9229.97	+	15986.8i	−0.690936	+	1.19674i	−0.971532	+	0.236910i	$0.923865\pi$
$564$		0			0
$565$	−59.8318	+	34.5439i	−0.00445512	+	0.00257217i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3033.11	+	1751.17i	−0.223471	+	0.129021i	−0.607556	−	0.794277i	$-0.707850\pi$
$569$	−3033.11	+	1751.17i	−0.223471	+	0.129021i	0.384086	+	0.923297i	$0.374517\pi$
$570$		0			0
$571$	5593.74	−	9688.63i	0.409966	−	0.710082i	−0.584920	−	0.811091i	$-0.698874\pi$
$571$	5593.74	−	9688.63i	0.409966	−	0.710082i	0.994885	+	0.101009i	$0.0322072\pi$
$572$		0			0
$573$	−4448.64	+	3486.15i	−0.324336	+	0.254164i
$574$		0			0
$575$		−	5027.06i		−	0.364596i
$576$		0			0
$577$	8346.61	+	4818.92i	0.602208	+	0.347685i	0.769910	−	0.638153i	$-0.220301\pi$
$577$	8346.61	+	4818.92i	0.602208	+	0.347685i	−0.167702	+	0.985838i	$0.553635\pi$
$578$		0			0
$579$	−7437.90	+	18487.3i	−0.533867	+	1.32696i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	413.825	+	716.765i	0.0293977	+	0.0509183i
$584$		0			0
$585$	3436.52	−	3579.53i	0.242876	−	0.252983i
$586$		0			0
$587$	−3998.01			−0.281117			−0.140559	−	0.990072i	$-0.544890\pi$
$587$	−3998.01			−0.281117			−0.140559	+	0.990072i	$0.544890\pi$
$588$		0			0
$589$	2640.63			0.184729
$590$		0			0
$591$	1194.86	+	8412.50i	0.0831641	+	0.585523i
$592$		0			0
$593$	−5716.00	−	9900.41i	−0.395832	−	0.685600i	0.597375	−	0.801962i	$-0.296210\pi$
$593$	−5716.00	−	9900.41i	−0.395832	−	0.685600i	−0.993207	+	0.116361i	$0.962877\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−20789.8	−	8364.25i	−1.42524	−	0.573411i
$598$		0			0
$599$	700.491	+	404.428i	0.0477818	+	0.0275868i	0.523701	−	0.851902i	$-0.324551\pi$
$599$	700.491	+	404.428i	0.0477818	+	0.0275868i	−0.475919	+	0.879489i	$0.657884\pi$
$600$		0			0
$601$		−	6813.76i		−	0.462461i	−0.972899	−	0.231231i	$-0.925725\pi$
$601$		−	6813.76i		−	0.462461i	0.972899	−	0.231231i	$-0.0742752\pi$
$602$		0			0
$603$	3105.66	−	12613.3i	0.209738	−	0.851830i
$604$		0			0
$605$	5094.74	−	8824.35i	0.342365	−	0.592993i
$606$		0			0
$607$	−2799.03	+	1616.02i	−0.187165	+	0.108060i	−0.590655	−	0.806924i	$-0.701130\pi$
$607$	−2799.03	+	1616.02i	−0.187165	+	0.108060i	0.403490	+	0.914984i	$0.367797\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4355.15	−	2514.44i	0.288364	−	0.166487i
$612$		0			0
$613$	6607.92	−	11445.2i	0.435385	−	0.754110i	−0.561942	−	0.827177i	$-0.689945\pi$
$613$	6607.92	−	11445.2i	0.435385	−	0.754110i	0.997327	+	0.0730673i	$0.0232788\pi$
$614$		0			0
$615$	3500.26	+	4466.64i	0.229503	+	0.292866i
$616$		0			0
$617$		−	23412.7i		−	1.52765i	−0.645422	−	0.763826i	$-0.723319\pi$
$617$		−	23412.7i		−	1.52765i	0.645422	−	0.763826i	$-0.276681\pi$
$618$		0			0
$619$	9042.06	+	5220.44i	0.587126	+	0.338977i	0.763960	−	0.645263i	$-0.223252\pi$
$619$	9042.06	+	5220.44i	0.587126	+	0.338977i	−0.176834	+	0.984241i	$0.556586\pi$
$620$		0			0
$621$	6220.38	−	8641.16i	0.401957	−	0.558386i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	1478.55	+	2560.92i	0.0946271	+	0.163899i
$626$		0			0
$627$	191.060	−	27.1370i	0.0121694	−	0.00172846i
$628$		0			0
$629$	−15771.3			−0.999747
$630$		0			0
$631$	−1116.76			−0.0704556			−0.0352278	−	0.999379i	$-0.511216\pi$
$631$	−1116.76			−0.0704556			−0.0352278	+	0.999379i	$0.511216\pi$
$632$		0			0
$633$	−14829.0	+	2106.22i	−0.931123	+	0.132251i
$634$		0			0
$635$	1483.93	+	2570.25i	0.0927372	+	0.160626i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−349.953	−	1207.08i	−0.0216650	−	0.0747285i
$640$		0			0
$641$	1197.94	+	691.630i	0.0738155	+	0.0426174i	0.536453	−	0.843930i	$-0.319764\pi$
$641$	1197.94	+	691.630i	0.0738155	+	0.0426174i	−0.462638	+	0.886547i	$0.653097\pi$
$642$		0			0
$643$		−	13841.5i		−	0.848918i	−0.905447	−	0.424459i	$-0.860464\pi$
$643$		−	13841.5i		−	0.848918i	0.905447	−	0.424459i	$-0.139536\pi$
$644$		0			0
$645$	6993.46	+	8924.27i	0.426926	+	0.544795i
$646$		0			0
$647$	−1188.54	+	2058.62i	−0.0722201	+	0.125089i	−0.899874	−	0.436150i	$-0.856342\pi$
$647$	−1188.54	+	2058.62i	−0.0722201	+	0.125089i	0.827654	+	0.561239i	$0.189675\pi$
$648$		0			0
$649$	−831.581	+	480.113i	−0.0502964	+	0.0290387i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4812.62	+	2778.57i	−0.288411	+	0.166514i	−0.637225	−	0.770678i	$-0.719918\pi$
$653$	−4812.62	+	2778.57i	−0.288411	+	0.166514i	0.348814	+	0.937192i	$0.386584\pi$
$654$		0			0
$655$	−5410.12	+	9370.60i	−0.322734	+	0.558992i
$656$		0			0
$657$	25250.4	+	6217.17i	1.49941	+	0.369185i
$658$		0			0
$659$			32145.5i			1.90017i	0.311991	+	0.950085i	$0.399004\pi$
$659$			32145.5i			1.90017i	−0.311991	+	0.950085i	$0.600996\pi$
$660$		0			0
$661$	−602.813	−	348.034i	−0.0354715	−	0.0204795i	0.482159	−	0.876084i	$-0.339853\pi$
$661$	−602.813	−	348.034i	−0.0354715	−	0.0204795i	−0.517631	+	0.855604i	$0.673186\pi$
$662$		0			0
$663$	−6830.34	−	2748.01i	−0.400103	−	0.160971i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	11459.6	+	19848.6i	0.665243	+	1.15223i
$668$		0			0
$669$	2468.65	+	17380.7i	0.142666	+	1.00445i
$670$		0			0
$671$	−716.485			−0.0412215
$672$		0			0
$673$	−12403.6			−0.710436			−0.355218	−	0.934783i	$-0.615593\pi$
$673$	−12403.6			−0.710436			−0.355218	+	0.934783i	$0.615593\pi$
$674$		0			0
$675$	930.819	−	9246.57i	0.0530774	−	0.527260i
$676$		0			0
$677$	−9752.83	−	16892.4i	−0.553666	−	0.958977i	−0.998006	−	0.0631191i	$-0.979895\pi$
$677$	−9752.83	−	16892.4i	−0.553666	−	0.958977i	0.444340	−	0.895858i	$-0.353438\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	9847.94	−	24477.6i	0.554146	−	1.37736i
$682$		0			0
$683$	−25452.0	−	14694.7i	−1.42591	−	0.823247i	−0.429111	−	0.903252i	$-0.641173\pi$
$683$	−25452.0	−	14694.7i	−1.42591	−	0.823247i	−0.996795	+	0.0800044i	$0.974507\pi$
$684$		0			0
$685$			5586.92i			0.311628i
$686$		0			0
$687$	−17875.0	+	14007.6i	−0.992682	+	0.777911i
$688$		0			0
$689$	7546.62	−	13071.1i	0.417276	−	0.722743i
$690$		0			0
$691$	27416.6	−	15829.0i	1.50937	−	0.871436i	0.509432	−	0.860511i	$-0.329856\pi$
$691$	27416.6	−	15829.0i	1.50937	−	0.871436i	0.999940	−	0.0109252i	$-0.00347768\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8380.40	+	4838.43i	−0.457391	+	0.264075i
$696$		0			0
$697$	4209.87	−	7291.72i	0.228781	−	0.396260i
$698$		0			0
$699$	−15752.7	+	12344.5i	−0.852392	+	0.667973i
$700$		0			0
$701$			5372.77i			0.289482i	0.989470	+	0.144741i	$0.0462349\pi$
$701$			5372.77i			0.289482i	−0.989470	+	0.144741i	$0.953765\pi$
$702$		0			0
$703$	−6528.59	−	3769.28i	−0.350257	−	0.202221i
$704$		0			0
$705$	−3118.36	+	7750.85i	−0.166587	+	0.414062i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	16713.7	+	28949.0i	0.885328	+	1.53343i	0.845337	+	0.534233i	$0.179400\pi$
$709$	16713.7	+	28949.0i	0.885328	+	1.53343i	0.0399911	+	0.999200i	$0.487267\pi$
$710$		0			0
$711$	−24572.9	−	23591.1i	−1.29614	−	1.24435i
$712$		0			0
$713$	7094.18			0.372621
$714$		0			0
$715$	241.620			0.0126379
$716$		0			0
$717$	−5164.40	−	36360.4i	−0.268993	−	1.89387i
$718$		0			0
$719$	13795.7	+	23894.9i	0.715567	+	1.23940i	0.962740	+	0.270428i	$0.0871651\pi$
$719$	13795.7	+	23894.9i	0.715567	+	1.23940i	−0.247173	+	0.968971i	$0.579502\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−14676.5	−	5904.73i	−0.754947	−	0.303734i
$724$		0			0
$725$	17324.6	+	10002.4i	0.887477	+	0.512385i
$726$		0			0
$727$		−	16801.8i		−	0.857143i	−0.903508	−	0.428572i	$-0.859017\pi$
$727$		−	16801.8i		−	0.857143i	0.903508	−	0.428572i	$-0.140983\pi$
$728$		0			0
$729$	13041.5	−	14742.4i	0.662578	−	0.748993i
$730$		0			0
$731$	8411.25	−	14568.7i	0.425583	−	0.737131i
$732$		0			0
$733$	14820.4	−	8556.57i	0.746800	−	0.431165i	−0.0777364	−	0.996974i	$-0.524769\pi$
$733$	14820.4	−	8556.57i	0.746800	−	0.431165i	0.824537	+	0.565809i	$0.191436\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	547.780	−	316.261i	0.0273782	−	0.0158068i
$738$		0			0
$739$	−9855.83	+	17070.8i	−0.490599	+	0.849742i	−0.999941	−	0.0108215i	$-0.996555\pi$
$739$	−9855.83	+	17070.8i	−0.490599	+	0.849742i	0.509342	+	0.860564i	$0.329889\pi$
$740$		0			0
$741$	−2170.69	−	2769.99i	−0.107614	−	0.137325i
$742$		0			0
$743$			17443.3i			0.861283i	0.902523	+	0.430642i	$0.141713\pi$
$743$			17443.3i			0.861283i	−0.902523	+	0.430642i	$0.858287\pi$
$744$		0			0
$745$	6266.59	+	3618.02i	0.308175	+	0.177925i
$746$		0			0
$747$	−21812.3	+	6323.75i	−1.06837	+	0.309737i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	9793.78	+	16963.3i	0.475872	+	0.824235i	0.999618	−	0.0276399i	$-0.00879916\pi$
$751$	9793.78	+	16963.3i	0.475872	+	0.824235i	−0.523746	+	0.851875i	$0.675466\pi$
$752$		0			0
$753$	−27982.5	+	3974.47i	−1.35424	+	0.192348i
$754$		0			0
$755$	−2357.45			−0.113638
$756$		0			0
$757$	−4635.88			−0.222581			−0.111291	−	0.993788i	$-0.535498\pi$
$757$	−4635.88			−0.222581			−0.111291	+	0.993788i	$0.535498\pi$
$758$		0			0
$759$	513.291	−	72.9047i	0.0245472	−	0.00348653i
$760$		0			0
$761$	9585.45	+	16602.5i	0.456600	+	0.790854i	0.998779	−	0.0494092i	$-0.0157338\pi$
$761$	9585.45	+	16602.5i	0.456600	+	0.790854i	−0.542179	+	0.840263i	$0.682400\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	11747.6	−	3405.83i	0.555211	−	0.160965i
$766$		0			0
$767$	15164.9	+	8755.47i	0.713916	+	0.412180i
$768$		0			0
$769$		−	22223.5i		−	1.04213i	−0.853517	−	0.521065i	$-0.825535\pi$
$769$		−	22223.5i		−	1.04213i	0.853517	−	0.521065i	$-0.174465\pi$
$770$		0			0
$771$	−7303.52	−	9319.93i	−0.341154	−	0.435342i
$772$		0			0
$773$	10497.8	−	18182.7i	0.488460	−	0.846037i	−0.511452	−	0.859312i	$-0.670892\pi$
$773$	10497.8	−	18182.7i	0.488460	−	0.846037i	0.999912	+	0.0132746i	$0.00422555\pi$
$774$		0			0
$775$	5362.50	−	3096.04i	0.248551	−	0.143501i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3485.40	−	2012.30i	0.160305	−	0.0925520i
$780$		0			0
$781$	30.5983	−	52.9979i	0.00140191	−	0.00242819i
$782$		0			0
$783$	17403.1	+	38630.5i	0.794299	+	1.76315i
$784$		0			0
$785$		−	14290.1i		−	0.649728i
$786$		0			0
$787$	−20245.5	−	11688.7i	−0.916994	−	0.529427i	−0.0343191	−	0.999411i	$-0.510926\pi$
$787$	−20245.5	−	11688.7i	−0.916994	−	0.529427i	−0.882675	+	0.469984i	$0.844260\pi$
$788$		0			0
$789$	5588.49	+	2248.39i	0.252162	+	0.101451i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	6533.01	+	11315.5i	0.292552	+	0.506715i
$794$		0			0
$795$	3526.08	+	24825.6i	0.157305	+	1.10752i
$796$		0			0
$797$	5445.93			0.242039			0.121019	−	0.992650i	$-0.461384\pi$
$797$	5445.93			0.242039			0.121019	+	0.992650i	$0.461384\pi$
$798$		0			0
$799$	12396.0			0.548858
$800$		0			0
$801$	−24976.1	−	23978.2i	−1.10173	−	1.05771i
$802$		0			0
$803$	633.118	+	1096.59i	0.0278235	+	0.0481916i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−7268.88	+	18067.2i	−0.317071	+	0.788099i
$808$		0			0
$809$	−28161.4	−	16259.0i	−1.22386	−	0.706597i	−0.258122	−	0.966112i	$-0.583104\pi$
$809$	−28161.4	−	16259.0i	−1.22386	−	0.706597i	−0.965739	+	0.259516i	$0.916437\pi$
$810$		0			0
$811$		−	16408.0i		−	0.710437i	−0.934783	−	0.355218i	$-0.884406\pi$
$811$		−	16408.0i		−	0.710437i	0.934783	−	0.355218i	$-0.115594\pi$
$812$		0			0
$813$	8367.31	−	6557.01i	0.360953	−	0.282859i
$814$		0			0
$815$	12422.7	−	21516.8i	0.533926	−	0.924787i
$816$		0			0
$817$	6963.76	−	4020.53i	0.298202	−	0.172167i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10550.2	+	6091.13i	−0.448481	+	0.258931i	−0.707188	−	0.707025i	$-0.750037\pi$
$821$	−10550.2	+	6091.13i	−0.448481	+	0.258931i	0.258707	+	0.965956i	$0.416703\pi$
$822$		0			0
$823$	−2231.32	+	3864.75i	−0.0945064	+	0.163690i	−0.909402	−	0.415917i	$-0.863461\pi$
$823$	−2231.32	+	3864.75i	−0.0945064	+	0.163690i	0.814896	+	0.579607i	$0.196794\pi$
$824$		0			0
$825$	356.181	−	279.120i	0.0150311	−	0.0117790i
$826$		0			0
$827$			2442.53i			0.102703i	0.998681	+	0.0513513i	$0.0163528\pi$
$827$			2442.53i			0.102703i	−0.998681	+	0.0513513i	$0.983647\pi$
$828$		0			0
$829$	−8327.05	−	4807.62i	−0.348866	−	0.201418i	0.315319	−	0.948986i	$-0.397888\pi$
$829$	−8327.05	−	4807.62i	−0.348866	−	0.201418i	−0.664186	+	0.747567i	$0.731222\pi$
$830$		0			0
$831$	−9393.09	+	23347.0i	−0.392109	+	0.974609i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	7746.43	+	13417.2i	0.321050	+	0.556074i
$836$		0			0
$837$	13048.7	+	1313.57i	0.538866	+	0.0542457i
$838$		0			0
$839$	−19611.2			−0.806979			−0.403489	−	0.914984i	$-0.632203\pi$
$839$	−19611.2			−0.806979			−0.403489	+	0.914984i	$0.632203\pi$
$840$		0			0
$841$	−66815.9			−2.73959
$842$		0			0
$843$	−604.988	−	4259.46i	−0.0247175	−	0.174026i
$844$		0			0
$845$	6217.39	+	10768.8i	0.253118	+	0.438413i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−41204.8	−	16577.7i	−1.66566	−	0.670136i
$850$		0			0
$851$	−17539.3	−	10126.3i	−0.706511	−	0.407904i
$852$		0			0
$853$			49160.6i			1.97330i	0.162848	+	0.986651i	$0.447932\pi$
$853$			49160.6i			1.97330i	−0.162848	+	0.986651i	$0.552068\pi$
$854$		0			0
$855$	5676.98	+	1397.79i	0.227074	+	0.0559104i
$856$		0			0
$857$	5684.31	−	9845.52i	0.226572	−	0.392435i	−0.730218	−	0.683215i	$-0.760581\pi$
$857$	5684.31	−	9845.52i	0.226572	−	0.392435i	0.956790	+	0.290780i	$0.0939147\pi$
$858$		0			0
$859$	−6120.51	+	3533.68i	−0.243107	+	0.140358i	−0.616604	−	0.787273i	$-0.711492\pi$
$859$	−6120.51	+	3533.68i	−0.243107	+	0.140358i	0.373497	+	0.927631i	$0.378159\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−23350.3	+	13481.3i	−0.921035	+	0.531760i	−0.883965	−	0.467553i	$-0.845136\pi$
$863$	−23350.3	+	13481.3i	−0.921035	+	0.531760i	−0.0370701	+	0.999313i	$0.511802\pi$
$864$		0			0
$865$	2685.17	−	4650.85i	0.105547	−	0.182813i
$866$		0			0
$867$	4552.54	+	5809.44i	0.178330	+	0.227565i
$868$		0			0
$869$		−	1658.68i		−	0.0647491i
$870$		0			0
$871$	−9989.45	−	5767.41i	−0.388610	−	0.224364i
$872$		0			0
$873$	453.199	+	1563.21i	0.0175698	+	0.0606031i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	19303.6	+	33434.9i	0.743258	+	1.28736i	0.951004	+	0.309177i	$0.100054\pi$
$877$	19303.6	+	33434.9i	0.743258	+	1.28736i	−0.207747	+	0.978183i	$0.566613\pi$
$878$		0			0
$879$	−37384.9	+	5309.92i	−1.43454	+	0.203753i
$880$		0			0
$881$	3460.09			0.132320			0.0661598	−	0.997809i	$-0.478925\pi$
$881$	3460.09			0.132320			0.0661598	+	0.997809i	$0.478925\pi$
$882$		0			0
$883$	10380.8			0.395631			0.197815	−	0.980239i	$-0.436615\pi$
$883$	10380.8			0.395631			0.197815	+	0.980239i	$0.436615\pi$
$884$		0			0
$885$	−28802.3	+	4090.91i	−1.09399	+	0.155383i
$886$		0			0
$887$	−22566.0	−	39085.4i	−0.854217	−	1.47955i	−0.877369	−	0.479815i	$-0.840704\pi$
$887$	−22566.0	−	39085.4i	−0.854217	−	1.47955i	0.0231523	−	0.999732i	$-0.492630\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	957.626	−	39.0561i	0.0360064	−	0.00146850i
$892$		0			0
$893$	5131.37	+	2962.60i	0.192290	+	0.111019i
$894$		0			0
$895$		−	21994.1i		−	0.821431i
$896$		0			0
$897$	−5831.65	−	7441.69i	−0.217071	−	0.277002i
$898$		0			0
$899$	−14115.3	+	24448.5i	−0.523663	+	0.907011i
$900$		0			0
$901$	32219.6	−	18602.0i	1.19133	−	0.687817i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−13106.6	+	7567.08i	−0.481411	+	0.277943i
$906$		0			0
$907$	−21491.9	+	37225.1i	−0.786800	+	1.36278i	0.141118	+	0.989993i	$0.454930\pi$
$907$	−21491.9	+	37225.1i	−0.786800	+	1.36278i	−0.927918	+	0.372785i	$0.878403\pi$
$908$		0			0
$909$	−7544.26	+	30640.2i	−0.275278	+	1.11801i
$910$		0			0
$911$		−	45726.0i		−	1.66297i	−0.555545	−	0.831487i	$-0.687490\pi$
$911$		−	45726.0i		−	1.66297i	0.555545	−	0.831487i	$-0.312510\pi$
$912$		0			0
$913$	−957.686	−	552.920i	−0.0347150	−	0.0200427i
$914$		0			0
$915$	−20138.2	−	8102.09i	−0.727593	−	0.292729i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	12581.6	+	21791.9i	0.451608	+	0.782208i	0.998486	−	0.0550040i	$-0.0175172\pi$
$919$	12581.6	+	21791.9i	0.451608	+	0.782208i	−0.546878	+	0.837212i	$0.684184\pi$
$920$		0			0
$921$	3013.93	+	21219.8i	0.107831	+	0.759191i
$922$		0			0
$923$	−1116.00			−0.0397980
$924$		0			0
$925$	−17677.4			−0.628355
$926$		0			0
$927$	342.627	−	356.886i	0.0121395	−	0.0126447i
$928$		0			0
$929$	10145.7	+	17572.8i	0.358309	+	0.620609i	0.987678	−	0.156497i	$-0.0500202\pi$
$929$	10145.7	+	17572.8i	0.358309	+	0.620609i	−0.629370	+	0.777106i	$0.716687\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	6396.92	−	15899.9i	0.224465	−	0.557920i
$934$		0			0
$935$	515.788	+	297.791i	0.0180407	+	0.0104158i
$936$		0			0
$937$		−	25708.8i		−	0.896339i	−0.893949	−	0.448170i	$-0.852076\pi$
$937$		−	25708.8i		−	0.896339i	0.893949	−	0.448170i	$-0.147924\pi$
$938$		0			0
$939$	−24502.5	+	19201.3i	−0.851555	+	0.667318i
$940$		0			0
$941$	−4571.93	+	7918.81i	−0.158385	+	0.274332i	−0.934287	−	0.356523i	$-0.883962\pi$
$941$	−4571.93	+	7918.81i	−0.158385	+	0.274332i	0.775901	+	0.630854i	$0.217296\pi$
$942$		0			0
$943$	9363.68	−	5406.12i	0.323354	−	0.186689i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−38004.7	+	21942.0i	−1.30411	+	0.752925i	−0.981105	−	0.193474i	$-0.938025\pi$
$947$	−38004.7	+	21942.0i	−1.30411	+	0.752925i	−0.323000	+	0.946399i	$0.604691\pi$
$948$		0			0
$949$	11545.7	−	19997.7i	0.394931	−	0.684040i
$950$		0			0
$951$	−29017.7	+	22739.6i	−0.989445	+	0.775374i
$952$		0			0
$953$		−	29621.5i		−	1.00686i	−0.864037	−	0.503429i	$-0.832072\pi$
$953$		−	29621.5i		−	1.00686i	0.864037	−	0.503429i	$-0.167928\pi$
$954$		0			0
$955$	−7220.70	−	4168.87i	−0.244666	−	0.141258i
$956$		0			0
$957$	−770.050	+	1914.00i	−0.0260106	+	0.0646509i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−10526.4	−	18232.2i	−0.353341	−	0.612004i
$962$		0			0
$963$	17812.3	−	18553.6i	0.596048	−	0.620853i
$964$		0			0
$965$	−29397.4			−0.980658
$966$		0			0
$967$	39437.0			1.31149			0.655744	−	0.754983i	$-0.272355\pi$
$967$	39437.0			1.31149			0.655744	+	0.754983i	$0.272355\pi$
$968$		0			0
$969$	−1219.85	−	8588.43i	−0.0404408	−	0.284727i
$970$		0			0
$971$	−11231.4	−	19453.3i	−0.371197	−	0.642931i	0.618553	−	0.785743i	$-0.287719\pi$
$971$	−11231.4	−	19453.3i	−0.371197	−	0.642931i	−0.989750	+	0.142812i	$0.954386\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−7655.86	−	3080.14i	−0.251470	−	0.101173i
$976$		0			0
$977$	−23589.9	−	13619.6i	−0.772474	−	0.445988i	0.0612826	−	0.998120i	$-0.480481\pi$
$977$	−23589.9	−	13619.6i	−0.772474	−	0.445988i	−0.833756	+	0.552132i	$0.813814\pi$
$978$		0			0
$979$		−	1685.90i		−	0.0550374i
$980$		0			0
$981$	4569.48	−	18558.5i	0.148718	−	0.604003i
$982$		0			0
$983$	−4358.40	+	7548.98i	−0.141416	+	0.244939i	−0.928030	−	0.372506i	$-0.878499\pi$
$983$	−4358.40	+	7548.98i	−0.141416	+	0.244939i	0.786614	+	0.617445i	$0.211832\pi$
$984$		0			0
$985$	−10855.5	+	6267.42i	−0.351152	+	0.202738i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	18708.4	−	10801.3i	0.601510	−	0.347282i
$990$		0			0
$991$	14888.8	−	25788.1i	0.477252	−	0.826625i	−0.522408	−	0.852696i	$-0.674966\pi$
$991$	14888.8	−	25788.1i	0.477252	−	0.826625i	0.999660	+	0.0260705i	$0.00829944\pi$
$992$		0			0
$993$	−29370.6	−	37479.4i	−0.938618	−	1.19776i
$994$		0			0
$995$		−	33058.7i		−	1.05330i
$996$		0			0
$997$	46504.6	+	26849.5i	1.47725	+	0.852890i	0.999670	−	0.0256990i	$-0.00818116\pi$
$997$	46504.6	+	26849.5i	1.47725	+	0.852890i	0.477579	+	0.878589i	$0.341514\pi$
$998$		0			0
$999$	−30386.1	−	21873.6i	−0.962337	−	0.692743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.4.k.e.521.22		48
3.2	odd	2	inner	588.4.k.e.521.15		48
7.2	even	3	inner	588.4.k.e.509.10		48
7.3	odd	6		588.4.f.d.293.20	yes	24
7.4	even	3		588.4.f.d.293.5	✓	24
7.5	odd	6	inner	588.4.k.e.509.15		48
7.6	odd	2	inner	588.4.k.e.521.3		48
21.2	odd	6	inner	588.4.k.e.509.3		48
21.5	even	6	inner	588.4.k.e.509.22		48
21.11	odd	6		588.4.f.d.293.19	yes	24
21.17	even	6		588.4.f.d.293.6	yes	24
21.20	even	2	inner	588.4.k.e.521.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.4.f.d.293.5	✓	24	7.4	even	3
588.4.f.d.293.6	yes	24	21.17	even	6
588.4.f.d.293.19	yes	24	21.11	odd	6
588.4.f.d.293.20	yes	24	7.3	odd	6
588.4.k.e.509.3		48	21.2	odd	6	inner
588.4.k.e.509.10		48	7.2	even	3	inner
588.4.k.e.509.15		48	7.5	odd	6	inner
588.4.k.e.509.22		48	21.5	even	6	inner
588.4.k.e.521.3		48	7.6	odd	2	inner
588.4.k.e.521.10		48	21.20	even	2	inner
588.4.k.e.521.15		48	3.2	odd	2	inner
588.4.k.e.521.22		48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	588.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.14452 - 0.730696i) q^{3} +(3.83273 + 6.63849i) q^{5} +(25.9322 - 7.51816i) q^{9} +O(q^{10})\)	\(q+(5.14452 - 0.730696i) q^{3} +(3.83273 + 6.63849i) q^{5} +(25.9322 - 7.51816i) q^{9} +(1.13857 + 0.657354i) q^{11} -23.9754i q^{13} +(24.5683 + 31.3513i) q^{15} +(29.5490 - 51.1804i) q^{17} +(24.4639 - 14.1243i) q^{19} +(65.7234 - 37.9454i) q^{23} +(33.1203 - 57.3661i) q^{25} +(127.915 - 57.6258i) q^{27} +302.001i q^{29} +(80.9549 + 46.7393i) q^{31} +(6.33773 + 2.54982i) q^{33} +(-133.433 - 231.113i) q^{37} +(-17.5187 - 123.342i) q^{39} +142.471 q^{41} +284.654 q^{43} +(149.300 + 143.335i) q^{45} +(104.876 + 181.651i) q^{47} +(114.618 - 284.890i) q^{51} +(545.190 + 314.765i) q^{53} +10.0779i q^{55} +(115.535 - 90.5383i) q^{57} +(-365.186 + 632.521i) q^{59} +(-471.964 + 272.488i) q^{61} +(159.160 - 91.8912i) q^{65} +(240.556 - 416.655i) q^{67} +(310.389 - 243.235i) q^{69} -46.5477i q^{71} +(834.095 + 481.565i) q^{73} +(128.471 - 319.322i) q^{75} +(-630.818 - 1092.61i) q^{79} +(615.955 - 389.924i) q^{81} -841.130 q^{83} +453.014 q^{85} +(220.671 + 1553.65i) q^{87} +(-641.169 - 1110.54i) q^{89} +(450.626 + 181.298i) q^{93} +(187.528 + 108.269i) q^{95} +60.2806i q^{97} +(34.4677 + 8.48666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 64 q^{9}+O(q^{10}) \) 48 * q + 64 * q^9	\( 48 q + 64 q^{9} - 192 q^{15} - 456 q^{25} + 432 q^{37} - 688 q^{39} + 1248 q^{43} + 1536 q^{51} - 2720 q^{57} + 528 q^{67} - 3744 q^{79} - 3408 q^{81} + 13824 q^{85} + 5088 q^{93} - 15472 q^{99}+O(q^{100}) \) 48 * q + 64 * q^9 - 192 * q^15 - 456 * q^25 + 432 * q^37 - 688 * q^39 + 1248 * q^43 + 1536 * q^51 - 2720 * q^57 + 528 * q^67 - 3744 * q^79 - 3408 * q^81 + 13824 * q^85 + 5088 * q^93 - 15472 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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